How to make the local level model with seasonal effect

Overview

On time-series analytics, we frequently need to think about a recurring pattern. In the context of time-series analytics, a recurring pattern is referred to as a seasonal effect.

For example, please see the image below. This image is the plotting of a time series data. As you can see, it has recurrent pattern.


On this article, I'll make the local level model with seasonal effects on Stan.

Simple trial of various types of time series analytics

By air passengers data, which is typical time-series data, I'll try some time-series analytics methods. Actually, about some points, I'm not sure if it is really appropriate or not. So, if you find some wrong or incorrect points, please let me know.

How to check autocorrelation on Python

To time series data, we usually check autocorrelation. As a memo, I’ll write down how to get the autocorrelation and the plot of it on Python.

Anti-pattern of the local level model with explanatory variable

Overview

On this article, I'll try anti-pattern of the local level model with explanatory variable.
Before, on the article, Local level model with explanatory variable to time series data on Stan , I made the local level model with explanatory variable to time series data. From the article, I set the model as followings.
$u_t \sim Normal(u_{t-1}, \sigma_ξ^2)$
$β_t \sim Normal(β_{t-1}, \sigma_τ^2)$
$y_t \sim Normal(u_t + β_t \times x_t, \sigma_e^2)$
There, I set state disturbances $σ_τ^2$ as zero. That’s because on the book, An Introduction to State Space Time Series Analysis (Practical Econometrics), it is written that these state disturbances are usually fixed on zero to establish a stable relationship between $y_t$ and $x_t$. This time, as experiment, I’ll try the model without setting $σ_τ^2$ as zero, meaning I’ll set $β_t$ as changeable.

Summary of local level model and local linear trend model to time series data

Overview

On this article, I’ll leave the summary about local level model and local linear trend model.
The both models are for time series analysis. Those are too simple to adapt for real data as they are. But those are very fundamental in many cases and by adding some other factors, those can become practical. So, here, I’ll leave rough memos about those.
As a text book, I’m using the following book. This article responds to chapters two and three.

Local Linear Trend Model for time series analysis on Stan

Overview

On this article, I’ll make the local linear trend model to artificial time series data by Stan. Before, I made a local level model on Stan on the article, Local level model to time series data on Stan.
By adding the slope variable to that model, I’ll make the local linear trend model.
I used this book as reference.

Local level model with explanatory variable to time series data on Stan

Overview

On this article, I'll make the local level model with explanatory variable to time series data on Stan.
Before, I made the simple local level model on Stan. In the practical situation, we frequently need to make model with some explanatory variables. So, I'll make simple local level model with explanatory variables here.
As a reference, I’m using the following book. This article is dealing with the chapter 5 of the book.

Time series analysis to predict future points on Stan

Overview

Before, I made the simple local level model to time series data. At that article, I just showed the sampled points traced the data. This time, I also do sampling to predict the following points of the data.



Roughly, on the image above, the blue points are data you already have and the red points are the predict target. The purpose of this article is to make model by blue points, data and predict red points, the values of future.

Local level model to time series data on Stan

Overview

On the articles below, I tried local level modeling to time series data on Edward and am still struggling.

Time series analysis on TensorFlow and Edward: local level model

Deep learning and Machine learning methods blog

Time series analysis on TensorFlow and Edward: local level model:P.S. 1

On the article below, I tried to analyze time series data with local level model. On Stan, I could do it before without problem. But on Edward and TensorFlow, I have been struggling. Deep learning and Machine learning methods blog From the situation above, although it doesn't work well yet, I got some progress.

On this article, I’ll express by Stan what I wanted on Edward. In a nutshell, I’ll write local level model to time series data on Stan.

Time series analysis on TensorFlow and Edward: local level model:P.S. 1

Overview

On the article below, I tried to analyze time series data with local level model. On Stan, I could do it before without problem. But on Edward and TensorFlow, I have been struggling.

Time series analysis on TensorFlow and Edward: local level model

Deep learning and Machine learning methods blog

From the situation above, although it doesn’t work well yet, I got some progress.

Time series analysis on TensorFlow and Edward: local level model

Overview

To review the time series analysis from the basic points, I tried to do state space modeling with TensorFlow and Edward. And I’m at a loss.
The main purposes are these two.

• review the time series analysis from the basic points
• try to check how to do that on Edward and TensorFlow